Button presses require Edit Access, no matter what the button is doing. More info: Separate permission for buttons and workflows - #6 by RonMakesSystems
In this scenario, I’d recommend a bit of a work-around.
Make a second “Task for Dev” Database that has a one-to-one relation to the Task. In this task, most fields should be lookups to the original Task except for the things you want to be editable (like the state) those will need to be synced up with automations to one another.
Then time-logs need to be linked to both Tasks and Task (not ideal, but needed for the button to work). Then give the dev access to the Task for Dev as editor.
Important note: You will still need to give them access to the “Task” as reader due to the way Rich Text Field lookups work. Lookups are visible to those with no access, but not rich text
I haven’t set it up or tested this, so this is just the thought process. Curious if it works out!